TY - GEN

T1 - Placing the largest similar copy of a convex polygon among polygonal obstacles

AU - Paul Chew, L.

AU - Kedem, Klara

N1 - Publisher Copyright:
© 1989 ACM 0-89791-318-3/89/0006/0094.

PY - 1989/6/5

Y1 - 1989/6/5

N2 - Given a convex polygon I and an environment consisting of polygonal obstacles, we find the largest similar copy of 1 that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if I is a convex k-gon and if Q has n corners and edges then we can find the placement of the largest similar copy of t in the environment Q in time O(k4 n λ4 (kn) log n), where λ4 is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of P in time 0 (k2n λ3 (kn) log n).

AB - Given a convex polygon I and an environment consisting of polygonal obstacles, we find the largest similar copy of 1 that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if I is a convex k-gon and if Q has n corners and edges then we can find the placement of the largest similar copy of t in the environment Q in time O(k4 n λ4 (kn) log n), where λ4 is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of P in time 0 (k2n λ3 (kn) log n).

UR - http://www.scopus.com/inward/record.url?scp=0347729324&partnerID=8YFLogxK

U2 - 10.1145/73833.73853

DO - 10.1145/73833.73853

M3 - Conference contribution

AN - SCOPUS:0347729324

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 167

EP - 174

BT - Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989

PB - Association for Computing Machinery

T2 - 5th Annual Symposium on Computational Geometry, SCG 1989

Y2 - 5 June 1989 through 7 June 1989

ER -